You generally can’t sue government employees for their actions on the job

He isn't a civil servant. He has neither budgetary nor hiring authority from Congress. He receives no salary. He was not vetted or approved by the Senate. As near as I can tell, he has no real standing as a government agent.

Basically, I think the reason you haven't heard about lawsuits yet is because they have not advanced far enough into the pipeline to be visible. The biggest question right now is just a question of standing. Right now, the lawsuits that you're hearing about were the earliest ones, and they didn't have a sufficient period of time to show that the plaintiffs were materially harmed by Musk's actions. That's beginning to shift, and I notice that Musk has been conspicuously more quiet in the last few weeks.

We may not like the specific example, but presidents do have the power to create parts of the executive branch by executive order.

DOGE is technically just a renaming and reorganizing of the "United States Digital Service" (which itself was created by executive order by President Obama).

There are some procedural rules governing who can be a named defendant in a claim against the government. When you sue a government agency for non-monetary relief, for example to compel an official to interpret a statute in a particular way or an action for an injunction, you would name the head of the agency as the defendant. However, DOGE isn't a real government agency and he isn't even the appointed head of whatever it is. Nevertheless, he's named as a defendant, along with DOGE and others in 50 cases so far. https://www.justsecurity.org/107087/tracker-litigation-legal-challenges-trump-administration/ Whether he can be sued personally if acting in an official capacity is a different question. Normally the government assumes responsibility for an official acting on its behalf.